Geodesic
On the Well-posedness of Some generalized Characteristic Cauchy Problems
J.-A. Marti1 ; V. Dévoué1 ; A. Delcroix2 ; E. Allaud1 ; H. Vernaeve3
1 Laboratoire CEREGMIA, Université des Antilles, Campus de Shoelcher BP 7209, 97275 Schoelcher Cedex, Martinique
2 Laboratoire CRREF, IUFM de Guadeloupe, Morne Ferret, BP 399, 97178 Abymes Cedex, Guadeloupe
3 Department of Mathematics, Ghent University, Building S22, Krijgslaan 281, B 9000 Gent, Belgium
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 89-99.

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By means of convenient regularization for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we show existence and uniqueness of the solution.
DOI : 10.1051/mmnp/201611207

J.-A. Marti 1 ; V. Dévoué 1 ; A. Delcroix 2 ; E. Allaud 1 ; H. Vernaeve 3

1 Laboratoire CEREGMIA, Université des Antilles, Campus de Shoelcher BP 7209, 97275 Schoelcher Cedex, Martinique
2 Laboratoire CRREF, IUFM de Guadeloupe, Morne Ferret, BP 399, 97178 Abymes Cedex, Guadeloupe
3 Department of Mathematics, Ghent University, Building S22, Krijgslaan 281, B 9000 Gent, Belgium 
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J.-A. Marti; V. Dévoué; A. Delcroix; E. Allaud; H. Vernaeve. On the Well-posedness of Some generalized Characteristic Cauchy Problems. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 89-99. doi : 10.1051/mmnp/201611207. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611207/

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